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Intensity, Magnitude, Location, and Attenuation in
India for Felt Earthquakes since 1762
Walter Szeliga
Central Washington University, [email protected]
Susan Hough
Stacey Martin
Roger Bilham
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Recommended Citation
Szeliga, W., et al. (2010). Intensity, magnitude, location, and attenuation in India for felt earthquakes since 1762. Bulletin of the
Seismological Society of America, 100(2), 570-584. DOI: 10.1785/0120080329
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Bulletin of the Seismological Society of America, Vol. 100, No. 2, pp. 570–584, April 2010, doi: 10.1785/0120080329
Ⓔ
Intensity, Magnitude, Location, and Attenuation in India
for Felt Earthquakes since 1762
by Walter Szeliga, Susan Hough, Stacey Martin, and Roger Bilham
Abstract
A comprehensive, consistently interpreted new catalog of felt intensities
for India (Martin and Szeliga, 2010, this issue) includes intensities for 570 earthquakes; instrumental magnitudes and locations are available for 100 of these events.
We use the intensity values for 29 of the instrumentally recorded events to develop
new intensity versus attenuation relations for the Indian subcontinent and the
Himalayan region. We then use these relations to determine the locations and magnitudes of 234 historical events, using the method of Bakun and Wentworth (1997).
For the remaining 336 events, intensity distributions are too sparse to determine magnitude or location. We evaluate magnitude and location accuracy of newly located
events by comparing the instrumental- with the intensity-derived location for 29 calibration events, for which more than 15 intensity observations are available. With few
exceptions, most intensity-derived locations lie within a fault length of the instrumentally determined location. For events in which the azimuthal distribution of intensities
is limited, we conclude that the formal error bounds from the regression of Bakun and
Wentworth (1997) do not reflect the true uncertainties. We also find that the regression
underestimates the uncertainties of the location and magnitude of the 1819 Allah Bund
earthquake, for which a location has been inferred from mapped surface deformation.
Comparing our inferred attenuation relations to those developed for other regions, we
find that attenuation for Himalayan events is comparable to intensity attenuation in
California (Bakun and Wentworth, 1997), while intensity attenuation for cratonic
events is higher than intensity attenuation reported for central/eastern North America
(Bakun et al., 2003). Further, we present evidence that intensities of intraplate earthquakes have a nonlinear dependence on magnitude such that attenuation relations
based largely on small-to-moderate earthquakes may significantly overestimate the
magnitudes of historical earthquakes.
Online Material: Table and figures depicting hypocenter locations with supporting
parameters and uncertainty.
Introduction
In 1996, Johnston (1996) used published intensity values to
derive attenuation parameters for the Indian subcontinent.
However, these intensity values were not consistently determined and were biased by the inclusion of observations influenced by liquefaction and by inattention to the effects of
building fragility, as was common to early reports. From
these data, Johnston (1996) derived relations between isoseismal area and earthquake magnitude.
More recently, a number of studies have carefully and
systematically reinterpreted available macroseismic data
for a number of important historical earthquakes. Ambraseys
and Jackson (2003) present intensity evaluations and approximate magnitudes for several early events in the Himalaya
Despite a written history extending more than three millenia, the location and magnitude of earthquakes in the Indian
subcontinent and its surroundings prior to 1900 remain largely
unquantified. The Martin and Szeliga (2010) catalog of 8339
felt reports of 570 earthquakes since 1636 permits this shortcoming to be addressed. More than 98% of the earthquakes in
the Martin and Szeliga (2010) catalog occurred after 1800 and
more than 50% since 1900. In this article, we quantify attenuation versus distance relationships for India, and from these we
determine the probable magnitudes and locations of earthquakes that occurred before the instrumental catalog.
Previous studies have undertaken similar investigations
using less complete data with variable and uncertain quality.
570
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
and southern Tibet (from the years 1411, 1505, 1555, 1713,
1751, 1803 and 1806). Ambraseys (2004) assigns intensity
values for a Bangladesh earthquake in 1664 and discusses the
location of an earthquake in Sindh in 1668. Ambraseys and
Douglas (2004) present reevaluated intensities from 43 earthquakes in northern India and use inferred felt areas to estimate attenuation.
Recent events, such as the 2001 Bhuj earthquake, have
been the subject of extensive, traditional, ground-based intensity surveying of damage and other effects (Pande and
Kayal, 2003). Additionally, Internet-based methods (Wald
et al., 1999a; Amateur Seismic Centre [see Data and
Resources section]) have now begun to yield objectively
determined intensity distributions for moderate and large
earthquakes through the use of standardized questionnaires.
Recent efforts notwithstanding, systematically and carefully determined intensities have remained lacking for both
moderate historical earthquakes and for most moderate and
large instrumentally recorded earthquakes in India. The new
Martin and Szeliga (2010) catalog of felt earthquakes and
intensities, compiled from extant records in colonial libraries
and newspaper accounts, provides a new, rich source of
information for the past two centuries. Intensity values in
this catalog were assessed from the original sources using
the European Macroseismic Scale 1998 (EMS-98; Grünthal
and Levret, 2001). This new catalog includes 234 historical
earthquakes, ranging in magnitude from 4 to 8.6, that we
judge to have a sufficient number of intensity observations
to permit the evaluation of their epicentral parameters. in the
electronic supplement The results of these evaluations are
shown Ⓔ in the electronic edition of BSSA.
This important new catalog provides the basis for determining intensity attenuation relations for India and for determining locations and magnitudes for historical events for
which sufficient macroseismic information exists. We conclude our study by discussing examples of four earthquakes
from the nineteenth century.
571
Ambraseys and Douglas, 2004). These methods assign epicentral locations and magnitudes based on the location of
maximum shaking and the areal extent of isoseismal
contours. In this study, we use the method of Joyner and
Boore (1993) to empirically derive intensity attenuation
relationships for the Indian subcontinent. The functional
form of the intensity attenuation relationship used in this
study is as follows:
I a bMw cR d logR;
(1)
where R is the hypocentral distance, Mw is the moment magnitude, and a, b, c, and d are constants to be determined.
Equation (1) is derived by assuming that intensity is logarithmically proportional to the energy density of a point source
(Howell and Schultz, 1975). The cR and d logR terms are
generally taken to reflect intrinsic attenuation and geometrical spreading, respectively, although in practice these two
terms are difficult to resolve independently.
A one-stage maximum-likelihood methodology is used
to derive the intensity attenuation relationship using 29 calibration events (Joyner and Boore, 1993). Our calibration
events consist of earthquakes since 1950 with more than 15
felt-intensity reports (Fig. 1). Although we give preference
to earthquakes with hypocenters in the Centennial Catalog
(Engdahl and Villasenor, 2002), we utilize other hypocentral
catalogs for more recent earthquakes. If an event is not listed
in the Centennial Catalog, we use hypocentral estimates from
the Bulletin of the International Seismological Centre (ISC)
and thereafter, the USGS National Earthquake Information
Center Monthly Hypocenter Data File (MHDF). Preferred
moment magnitude estimates are from the Global Centroid
Moment Tensor Project (CMT). If an event is not listed in the
Data and Methods
The intensity values from the Martin and Szeliga (2010)
catalog used to derive the attenuation relationships for this
study reveal significant scatter at all distances. Although
some of this scatter is expected to result from imprecision
in intensity assignments (e.g., where structural fragility cannot be adequately assessed), rich, objectively determined
intensity distributions (e.g., Wald et al., 1999b; Atkinson
and Wald, 2007) reveal that intensities do vary substantially
as a consequence of local site geology and other factors.
Because there are unknown variations in the precise location
of repeated observations, the calculation of meaningful site
corrections is not possible. We thus do not consider site corrections in our analysis.
Previous studies of intensity attenuation in the Indian
subcontinent have used methods based on the area contained
within a contour of specific intensity (e.g., Johnston, 1996;
Figure 1.
Epicentral locations of 29 calibration events. We have
excluded earthquakes with depths in excess of 40 km. Diamonds,
events used to determine cratonic attenuation; circles, events used to
determine Himalayan attenuation.
572
W. Szeliga, S. Hough, S. Martin, and R. Bilham
Global CMT, we use moment magnitude estimates from the
Centennial Catalog, ISC, or the MHDF, in decreasing order of
preference (see Data and Resources section). For five calibration events (4:1 < M < 5:3), only body-wave magnitude
(mb ) estimates were available. Converting these body-wave
magnitudes to moment magnitudes using a published linear
relationship resulted in attenuation relationship coefficients
that were statistically indistinguishable from the uncorrected
magnitudes. We therefore have chosen to retain the original
body-wave magnitudes during inversion. For the largest
event in the catalog, the 1950 Chayu earthquake in eastern
Assam, we use the hypocentral location and magnitude listed
in Chen and Molnar (1977).
We first use a least squares approach to estimate parameters a d in equation (1), using the magnitude of all calibration earthquakes as well as the hypocentral distance to
each observation. The least squares inversion is weighted
by a covariance matrix that includes off-diagonal terms that
account for intraearthquake observational variance. The inversion is performed by inverting the normal equations with
the off-diagonal terms in the covariance matrix being determined using a maximum-likelihood methodology.
Utilizing the attenuation relation derived from the methods outlined previously, we then use the method outlined in
Bakun and Wentworth (1997) to determine epicenters and
magnitudes. For each earthquake we create a 5° × 5° grid
of trial hypocenters centered on the instrumentally determined hypocenter with a grid spacing of 5 arc-minutes. If
no instrumental hypocenter is available, we use the geometrical centroid of all of the intensity observations weighted by
their EMS-98 value and a depth of 15 km. For each trial
hypocenter, we calculate the slant distance to each intensity
observation and solve equation (1) for Mw. A weighted
measure of the dispersion of the magnitude estimates is then
calculated at each grid point using the following equation:
11
0P
2 2
W i Mi M
C
B
P 2
(2)
σ@ i
A
Wi
i
with
Wi Δi π
0:1 cos 2150
0:1
Δi < 150 km
;
Δi > 150 km
where Δi is the distance from the trial hypocenter to each
intensity observation i, Mi is the magnitude estimated from
is the mean magnitude
equation (1) for observation i, and M
at the trial epicenter. We then choose the trial epicenter that
minimizes equation (2) as the preferred epicentral estimate
as the preferred magnitude estimate.
and its associated M
In a scenario where all intensity observations are given equal
weight, (i.e., choosing W i 1:0 for all Δi ), equation (2)
becomes the sample standard deviation. Thus, the trial epicenter that minimizes equation (2) will be referred to as the
minimum deviation epicenter.
In general, intensity observations show a rapid decay
close to the epicenter; this behavior indicates that intensity
observations near the epicenter are more sensitive to the epicentral location and magnitude than are observations farther
away. Thus, we choose a function, W i , that gives greater
weight to observations that are closer to the trial epicenter.
While Bakun and Wentworth (1997) note that the 150 km
cutoff distance chosen for the weighting function is arbitrary,
we retain this value to facilitate direct comparison of our
results with those of Bakun and Wentworth (1997). A
possible benefit of retaining a cutoff distance of 150 km is
that it down-weights potentially magnified observations that
may result from critically reflected seismic phases, such as
SmS. In India, Moho depths vary from greater than 50 km on
the craton (Gupta et al., 2003) to 40 km beneath the Himalaya (Monsalve et al., 2008). Given a hypocentral depth of
15 km, one could reasonably expect SmS to first appear
between 120 and 150 km from an epicenter.
Results
We calculate separate attenuation parameters for earthquakes in the subcontinent (craton) and the Himalaya, in
addition to evaluating the parameters for the entire data
set (Table 1). Additionally, Figure 2 shows the distribution
of intensity data used to calculate the attenuation parameters
as a function of moment magnitude.
To investigate the self-consistency of our results, we utilize a cross-validation scheme (Efron and Tibshirani, 1993)
to characterize the predictive ability of our data set. We determine attenuation relationships using subsets of 21 instrumentally recorded calibration events randomly chosen without
replacement from our original list of 29 calibration events.
We then use the resulting attenuation relationship to determine the locations and magnitudes of the remaining eight
calibration events. This procedure is repeated to create
100 cross-validation samples. The resulting statistics show
a median epicentral misfit of 53 km and a magnitude misfit
of 0.38 Mw .
Table 1
Intensity Attenuation Relationship Parameters for India, the Indian Craton, and the Himalaya
Province
Number of Events
a*
b*
c*
d*
India
Craton
Himalaya
29
17
12
5:57 0:58
3:67 0:79
6:05 0:94
1:06 0:07
1:28 0:10
1:11 0:10
0:0010 0:0004
0:0017 0:0006
0:0006 0:0006
3:37 0:25
2:83 0:30
3:91 0:38
*Columns a, b, c, and d refer to the variables in equation (1).
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
(a)
9
(b)
9
573
Assam 1951
Himalaya EMS−98 data
8
8
Craton EMS−98 data
Bhuj 2001
Moment Magnitude
Moment Magnitude
Kashmir 2005
7
6
5
6
5
4
4
3
7
1
10
100
3
1000
1
10
100
1000
Distance to Centroid (km)
Distance to Centroid (km)
Figure 2. Intensity distributions for the data used to calculate the attenuation parameters in Table (1). (a) Distance to earthquake centroid
versus moment magnitude for events in the Himalaya. (b) Distance to earthquake centroid versus moment magnitude for events on the craton.
As noted, previous macroseismic studies in the Himalaya have used the areal extent of isoseismal radii to develop
attenuation relationships (Ambraseys and Douglas, 2004).
Figure 3 shows a comparison of these results with the
attenuation relationship developed here for the Himalaya.
While the attenuation relationship developed in this study
disagrees with that derived by Ambraseys and Douglas (2004)
at the 2 σ level (Table 2), the two attenuation relationships
are not grossly inconsistent for intensities greater than IV.
Both relationships appear to parallel each other before diverging below intensity III. We consider the sharp divergence
between these relationships below intensity III to be caused
by differences in the definition of the radius of perceptibility
between the EMS-98 scale and the Medvedev–Sponheuer–
Karnik (MSK) scale. In fact, the two attenuation relationships
can be brought into excellent agreement by either decrementing the value of a in our study by 0.5 intensity units or decreasing the epicentral distance by 25 km. Reasons for this shift
between the relationships could include the use of half-unit
intensities in Ambraseys and Douglas (2004), a slight bias
in assessed intensities between the two studies, variations
in the precision of the epicentral locations of the calibration
events between the studies, and differences in the methodology used to calculate the calibration curves.
Of these possibilities, we can only test for the presence
of a bias between the two data sets. We have compiled a
direct comparison of 95 intensities from three earthquakes
with common locations in both the Martin and Szeliga
(2010) catalog and Ambraseys and Douglas (2004) (Fig. 4).
This comparison indicates that the two studies are in good
statistical agreement, with more than 88% of the assessed
intensities differing by no more than one intensity unit.
Although none of these earthquakes are used in the generation of the calibration curves in Martin and Szeliga (2010)
and most assessed intensities are identical between studies
(ΔIntensity 0), this comparison shows that there appears
to be a slight bias toward lower values in the Martin and
Szeliga (2010) catalog by no more than one intensity unit.
Because a bias toward lower values in intensities in the
Martin and Szeliga (2010) catalog would require incrementing the value of a, we may rule out the possibility that a systematic bias is responsible for the discrepancy between the
two attenuation relationships.
8
7
6
Intensity
Comparisons with Previous Attenuation Studies
5
this study
4
3
2
Ambraseys and Douglas (2004)
1
0
200
400
600
800
1000
Distance (km)
Figure 3. Intensity attenuation with distance for a hypothetical
M 6.5 Himalayan earthquake from this study (solid line) and from
Ambraseys and Douglas (2004) (dashed line). Intensity data from
this study are in EMS-98, and data from Ambraseys and Douglas
(2004) are in MSK. Error bars are 2 σ. (See Table 2.)
574
W. Szeliga, S. Hough, S. Martin, and R. Bilham
10
Frequency
4
0
25
50
1803 Uttarkhand
1819 Allah Bund
1833 Nepal
3
8
1
E. North America (Bakun et al., 2003)
7
Intensity
∆ Intensity
2
9
6
CEUS (Atkinson and Wald, 2007)
5
4
0
3
−1
2
−2
this study
1
−3
−4
0
1
2
3
4
5
6
7
8
Figure 4. Comparison of assessed intensities at 95 common
locations from Martin and Szeliga (2010) and Ambraseys and
Douglas (2004) for three earthquakes. The x-axis (top) corresponds
to the normalized frequency of the combined intensity differences.
For individual earthquakes, the x-axis (bottom) corresponds to the
assessed intensity value from the Martin and Szeliga (2010) catalog.
The y-axis corresponds to the difference between the assessed
intensities from Martin and Szeliga (2010) and those from Ambraseys and Douglas (2004), with negative values indicating that the
intensity from Martin and Szeliga (2010) is lower than that listed in
Ambraseys and Douglas (2004). For clarity, intensities for the 1819
Allah Bund and 1833 Nepal earthquakes have been artificially
offset to the right by 0.1 and 0.2 intensity units respectively.
It has generally been assumed, based on overall similarities between the crustal structure and age of eastern North
America and India, that the regions are characterized by
similar attenuation of seismic waves and intensities (Johnston, 1996; Talwani and Gangopadhyay, 2000; Ellis et al.,
2001). However, previous authors have inferred systematic
differences in both peak ground motion attenuation and
weak-motion attenuation between eastern North America
and other stable continental regions worldwide (Bakun and
McGarr, 2002; Miao and Langston, 2008). Both Bakun et al.
(2003) and Atkinson and Wald (2007) have developed relationships between intensity and epicentral distance for eastern North America (Table 2). Figure 5 compares intensity
attenuation relationships in India with those from eastern
North America for a hypothetical Mw 6.5 earthquake. For
all epicentral distances, the attenuation relationship of Bakun
et al. (2003) predicts higher intensity observations in eastern
North American compared to cratonic India. In contrast, the
relationship developed by Atkinson and Wald (2007) agrees
with that for cratonic India above intensity V but below intensity V, and these two relationships diverge sharply, with
larger intensity values being predicted to greater distances in
eastern North America. This could be due to differences in
gross crustal properties between eastern North American and
cratonic India such that higher-mode surface waves (Lg)
travel more efficiently in eastern North America. However,
400
600
800
1000
1200
1400
Distance (km)
9
EMS−98 Intensity
200
Figure 5.
Comparison of the intensity attenuation relationships
from this study for India, from Bakun et al. (2003) for eastern North
America, and from Atkinson and Wald (2007) for the central eastern
United States (CEUS) for a hypothetical M 6.5 earthquake. Indian
intensity data are in EMS-98, while data from eastern North
America are in Modified Mercalli Intensity (MMI). Error bars
are 2 σ. (See Table 2.)
we note that Atkinson and Wald (2007) assume a different
functional form for intensity attenuation, one that includes
nonlinear magnitude terms.
A comparison of our results with the results of Bakun
et al. (2003) could be complicated by uncertainties associated with their results. In particular, the intensity values
for calibration events used by Bakun et al. (2003) have not
been systematically reinterpreted and may suffer from the
same problems that formerly plagued available intensity
values for India. To further investigate the difference revealed
in Figure 5, we directly compare attenuation from earthquakes of similar magnitude in eastern North America and
cratonic India. For low magnitude earthquakes (M ∼ 4:5), the
median distance at which shaking of intensity III and IV is
felt is twice as far in eastern North America as compared with
cratonic India (Fig. 6). These direct comparisons corroborate
the result that attenuation is at least a factor of 2 lower in
eastern North America compared to cratonic India.
While both the Himalaya and California are active plate
boundary zones, there is no reason to expect good agreement
in intensity attenuation between the two regions. Nonetheless
it is interesting to compare the results for these two regions.
Our results suggest that intrinsic attenuation is small
(c 0:0006 in equation 1) in the Himalayan region, which
is in agreement with the results of Atkinson and Wald (2007)
(their equivalent of c has a value of 0:0007), while Bakun
and Wentworth (1997) developed the California relationship
using 22 calibration events under the assumption that intrinsic attenuation was negligible (c 0 in equation 1) (Table 2).
This low intrinsic attenuation is indicative of a highly absorptive crust (high attenuation, low Q) which is expected in a
tectonically active region. Allowing for a vertical shift of
up to 0.5 intensity units due to differences in the intensity
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
(a)
7
(b)
7
29 Apr 2003 Fort Payne, AL (M 4.6)
6
6
5
5
Intensity
Intensity
18 Apr 2008 Mt. Carmel, IL (M 5.2)
4
3
575
4
3
2
2
26 Nov 2007 Delhi (M 4.7)
5 Sep 2000 Koyna (M 5.2)
1
1
0
250
500
750
0
250
500
750
Distance (km)
Distance (km)
Figure 6. A direct comparison of intensity observations between eastern North America and cratonic India. Eastern North American
intensity data are from the USGS Community Internet Intensity Map Project; error bars represent standard error estimates of the sample
median. (a) Direct comparison of the median distance to which each intensity was observed for the 18 April 2008 Mw 5.2 Mt. Carmel,
Illinois, earthquake and the 5 September 2000 Mw 5.2 Koyna earthquake. For intensities III–VI, the median distance is statistically larger for
the Mt. Carmel, Illinois, earthquake. (b) Direct comparison of the median distance to which each intensity was observed for the 29 April 2003
Mw 4.6 Fort Payne, Alabama, and the 26 November 2007 Mw 4.7 Delhi earthquake. Although the Delhi earthquake is larger than the Fort
Payne earthquake, the median distance to which intensities II–V are felt is smaller in India. This suggest that the attenuation difference
between eastern North American and India is equivalent to a magnitude increase of at least 0.2 Mw .
scales utilized, Figure 7 illustrates remarkably good agreement between both the Californian and the Himalayan intensity attenuation relationships.
Estimation of Historical Epicenters and Magnitudes
The precise locations of historical earthquakes in India
and the Himalaya have important consequences for recurrence interval studies as well as seismic hazard assessment.
Using the intensity attenuation relationships derived in the
preceding section, we determine the locations and magnitudes of historical events, examine the uncertainties of epi10
9
Intensity
8
7
this study
6
5
California (Bakun and Wentworth, 1997)
4
3
2
California
(Atkinson and Wald, 2007)
1
0
200
400
600
800
1000
1200
1400
Distance (km)
Figure 7. Intensity attenuation relationships for the
Himalaya from this study, the results of Bakun and Wentworth
(1997) for California, and the results from Atkinson and Wald
(2007) for California for a hypothetical M 6.5 earthquake. Indian
intensity data are in EMS-98 while data from California are in MMI.
(See Table 2.)
central locations and magnitudes, assess the completeness of
our catalog, and take a closer look at four historical earthquakes that have previously been interpreted as great
earthquakes. Maps showing the location and magnitude of
historical earthquakes calculated using data from the Martin
and Szeliga (2010) catalog are shown Ⓔ in the electronic
edition of BSSA. Finally, we use the intensity distribution
for the 2001 Bhuj earthquake to investigate what one would
infer for this event had it been known only from historical
sources.
Epicentral Locations and Magnitudes
of Historical Events
For earthquakes prior to 1890, the only information
available to us for assessing the location and magnitude
of most historical earthquakes in India comes from feltintensity data. The exceptions are for those earthquakes
whose location can be constrained from independent observations such as tide gauge data (e.g., the 1881 Car Nicobar
earthquake; Ortiz and Bilham, 2003), documented surface
rupture (e.g., the June 1505 central Himalayan earthquake
for which surface slip has been measured; Yule, personal
commun, 2007), and obvious surface deformation (e.g.,
the 1819 Allah Bund earthquake; Oldham, 1926), which
caused local uplift and a large region of subsidence).
The Martin and Szeliga (2010) catalog affords us the possibility of refining both the location and magnitude of many
earthquakes in the historical record. Although the approach
outlined in Data and Methods offers a sophisticated method
to quantitatively evaluate a probable epicentral location and,
with it, a probable magnitude, we have found that the Bakun
and Wentworth (1997) algorithm frequently chooses erroneous values where the results can be compared with instrumental values. For 100 test earthquakes for which we have
576
W. Szeliga, S. Hough, S. Martin, and R. Bilham
both intensity data and an instrumental location and magnitude, the median location error is 120 km with a median magnitude overprediction error of Mw 0.4.
The reason for the errors in location follows partly from
a paucity of observations and their spatial coverage, partly
from the absence of a large range of intensity values in a
given earthquake, and partly from the measure of dispersion
chosen as our metric in equation (2). Even for some very
well-recorded earthquakes that do not have these shortcomings, the estimated epicentral location is often counterintuitive and, where we can test its true location, demonstratively
incorrect. Examples are discussed subsequently. It may be
possible to decrease the discrepancies in epicentral location
and magnitude by choosing a measure of dispersion that is
more robust than equation (2) in the presence of outliers.
Where azimuthal felt-intensity coverage is limited to one
quadrant or to two contiguous quadrants from the epicenter,
as, for example, in earthquakes near the coast or on the southern edge of the Tibetan plateau (where reporting is inevitably
one sided), there is often a trade-off between magnitude and
location. We found that location accuracy in such cases can
be improved by selecting the preferred hypocentral location
to coincide with the location of the minimum magnitude, M,
from equation (2). This minimum magnitude location rarely
corresponds to the minimum deviation location determined
using equation (2). Lest too much credibility be attached to
the coordinates derived from the minimum deviation solution, we also list coordinates for the minimum magnitude
in Ⓔ Table S1 of the electronic edition of BSSA. The mean
location error using the minimum magnitude location as a
conservative constraint more than halves the misfit for the
100 test earthquakes to 44 km in position; however, this
method also systematically underpredicts earthquake magnitudes by Mw 0.6.
As an example, we show the location errors from the
minimum deviation method for aftershocks following the
10 December 1967 Koyna earthquake and nearby earthquakes (Fig. 8a). Some earthquakes were misplaced out to
sea, or far inland, with a median mislocation error of 120 km.
For some aftershocks, magnitudes are estimated to be larger
than the mainshock. In contrast, the location of the minimum
magnitude yields a median mislocation error of 26 km
(Fig. 8b), with magnitudes that were within 0.35 Mw of their
instrumental values. For earthquakes with more than 100 felt
observations, the location error is less than or equal to the
grid spacing (∼9 km).
While it is clearly to some extent a subjective decision
whether to use the minimum magnitude or the minimum
deviation solution, we note that choosing the minimum magnitude is consistent with the probability that, had the magnitude been larger, in many cases it would have been felt
by people in other quadrants.
In a search for a simple discriminant to reject aberrant
solutions, we found that the most accurate locations (within
30 km of the epicenter) are those for which the locations
chosen by equation (2) and the minimum magnitude location
differ by less than 30 km. However, if one were to apply
this criterion strictly, one would reject the locations of more
than two-thirds of the earthquakes. We prefer to include
solutions for a larger set of events, but it is important to note
the uncertainties discussed previously when utilizing our
solutions.
(a) 20˚00'
(b) 20˚00'
Thane
Thane
Marathwada
Marathwada
Killari
17˚30'
17˚30'
Koyna
Koyna
50 km
50 km
15˚00'
15˚00'
73˚
74˚
75˚
76˚
77˚
73˚
74˚
75˚
76˚
77˚
Figure 8. Comparison of the epicentral misfit for instrumentally recorded earthquakes in the Koyna region of India. On both figures, the
arrow points from the instrumental epicenter toward the intensity-derived epicenter. (a) Epicentral misfit in the Koyna region using
the location of the minimum of equation (2) as the epicentral estimate. (b) Epicentral misfit in the Koyna region using the location of
from equation (2).
the minimum M
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
Catalog Completeness
Log10(Number of earthquakes per year)
Using the magnitudes we have calculated for 234 events
in the Martin and Szeliga (2010) catalog, we compare their
magnitude distribution to the magnitude distribution from
the ISC catalog covering the same geographic region during
the period 1980–2000 (Fig. 9, see Data and Resources
section). Two first-order observations are apparent: (1) the
earthquake listing in the Martin and Szeliga (2010) catalog
appears to be significantly incomplete even for Mw 7.5, and
(2) there appear to be too many earthquakes with Mw > 8.
To investigate the extent to which missing aftershocks
from large earthquakes might be responsible for the incompleteness of the catalog below Mw 7.5, we remove known
aftershocks from the catalog. Then for each earthquake, we
add aftershocks according to a Gutenberg–Richter distribution (Gutenberg and Richter, 1954), with the largest aftershock in each sequence being 1.2 units smaller than its
mainshock (Båth, 1965). The resulting distribution is significantly closer to the distribution inferred from the ISC catalog,
although the distribution of events still appears to be incomplete by a factor of 3 for Mw 7, and a factor of 5 for Mw 5.
The overabundance of earthquakes with Mw > 8 is
likely due to tendency of the minimum deviation method
to overpredict magnitude by nearly Mw 0.4. Although some
of the catalog incompleteness above Mw 7 could be remedied
by adjusting higher magnitudes downward, it is impossible
to determine precisely which historical earthquakes have
inflated magnitudes. As a result, it is not possible to correct
for this bias. However, this bias cannot account for missing
earthquakes with Mw < 6; we therefore conclude that a substantial number of earthquakes are missing from the historical record. This result is not surprising, given the especially
4
1980−2000 ISC
Historical Data + G-R Aftershocks
Historical Data, no aftershocks
log10 (N) = 6.97 - 1.0 Mw
3
2
1
0
-1
-2
-3
4
5
6
7
8
9
Mw
Figure 9. Frequency–magnitude plot of earthquakes occurring
on the Indian subcontinent. Filled circles, events from the ISC
catalog during 1980–2000; diamonds, events from the Martin
and Szeliga (2010) catalog; open circles, with synthetic aftershock
sequences from a Gutenberg–Richter distribution added as described in section "Catalog Completeness"; dashed line represents
a frequency–magnitude relationship with a b value of 1.0.
577
scanty early historical record that is available for some of the
remote parts of our study area. Nonetheless, assuming it is
reasonable to include missing aftershocks, the distribution of
magnitudes provides a basis for quantification of overall
earthquake rates for seismic hazard assessment.
Recent studies have identified surface scarps that appear
to have been generated by extremely large megathrust earthquakes (e.g., Lavé et al., 2005; Kumar et al., 2006). One can
use the inferred magnitude-frequency distribution to explore
the expected rate of events that are larger than those in the
historical record. Using a maximum-likelihood method
(Bender, 1983) to fit the ISC results for Mw ≤ 7:5 and our results for larger events, we infer log10 N 7:17 1:034M.
Although at some point one expects a simple linear extrapolation to not be valid, this equation predicts one Mw 9.5 event
in the region on the order of once every 450 years.
Case Studies
The 1803 Uttarakhand Himalaya Earthquake
On 1 September 1803, a large earthquake shook much of
the central Himalaya and nearby Ganges plains, causing
severe damage to the town of Uttarkashi (Barahat). This
earthquake is famous for its alleged damage to the Qutab
Minar in Delhi, a structure that had stood, undamaged, since
its construction in the thirteenth century. This earthquake is
described briefly by Mallet and Mallet (1858) and Oldham
(1883). While Seeber and Armbruster (1981) consider it
the first of four great, colonial Himalayan earthquakes, no
quantitative evaluation of this earthquakes magnitude was
attempted before Ambraseys and Jackson (2003), who compiled intensity reports from over 30 locations and assigned a
tentative magnitude of MS 7.5. Subsequent authors (Ambraseys and Douglas, 2004; Rajendran and Rajendran, 2005)
also assigned magnitudes in the mid-7s using both Frankel’s
method (Frankel, 1994) and an isoseismal area method
tailored to India. Ambraseys and Douglas (2004) assign an
epicentral location near the Tibetan border (31.5° N, 79.0° E),
while Rajendran and Rajendran (2005) assign an epicentral
location near Srinagar (Sirmur) based on the region of maximum shaking intensity. Using the methods outlined in Data
and Methods, we assign a magnitude of M 7.3 with an intensity center (epicentral location) of 30.656° N, 78.784° E
(Fig. 10). Our preferred epicentral location lies 9 km south of
the 1991 M 6.8 Uttarkashi earthquake and 65 km west
of the 1999 M 6.6 Chamoli earthquake. Our study confirms
that this was not a great earthquake, despite it being
reported in numerous locations throughout the Ganges Plain.
The surprising proximity of the 1803 and 1991 earthquakes
is suggestive that one may be a recurrence of the other.
In 188 years, the present day convergence rate would result
in a slip deficit of greater than 3 m, more than sufficient to
drive an M 6.8 earthquake (Jade et al., 2004).
578
W. Szeliga, S. Hough, S. Martin, and R. Bilham
The 1819 Allah Bund Earthquake
The 16 June 1819 Allah Bund earthquake is one of the
earliest events with well-documented surface faulting (Oldham, 1926) and was responsible for the formation of Lake
Sindri, a 20 km north–south by 30 km east–west basin in
the northwestern Rann of Kachchh. Upon formation, the lake
flooded the village of Sindri and destroyed a fort of the same
name. Simultaneously, a region with 6 km north–south width
and with an inferred east–west length of 50–80 km rose and
dammed the Puram River for several years before a flood
incised the uplifted region and the river reoccupied its old
channel. This raised region was named the Allah Bund
(literally, dam of God) to distinguish it from the several
artificial dams across the Puram River (Oldham, 1926).
Although both the amplitude and extent of surface deformation in 1819 has been questioned (Rajendran and Rajendran,
2001), the sense of the observed surface uplift and subsidence provides an approximate constraint on the mechanism
and magnitude of the earthquake (7:7 0:2), from which an
epicenter several kilometers north of the Allah Bund has
been proposed (Bilham, 1998).
Less than 200 years later, the occurrence of a second
large earthquake on the Kachchh mainland, the 2001 Bhuj
earthquake (Mw 7.6), provided a much denser sampling of
over 350 felt reports Martin and Szeliga (2010) and Pande
and Kayal, 2003). The similarity of these reports to the felt
reports of the 1819 earthquake caused Hough et al. (2002) to
conclude that the 1819 and 2001 earthquakes were of similar
magnitude. In contrast, Ambraseys and Douglas (2004) list
the 1819 earthquake as being much larger (Mw 8.2), although
they note that no detailed reevaluation of the earthquake was
undertaken.
When applied to the 1819 intensity data, the algorithm
outlined in Data and Methods unexpectedly identifies an epicentral location 40 km northeast of the 2001 Bhuj epicenter
(Fig. 11). This location is 100 km east of the channel incised
through the Allah Bund first described by (Burnes, 1835) and
close to the mapped Island Belt fault (Fig. 11). The intensitybased magnitude for the 1819 earthquake is thus larger and the
epicenter more to the east than those estimated from geological or geodetic interpretations adopted in previous studies. In
contrast to the Koyna aftershocks discussed earlier, the minimum magnitude solution lies south of the Kachchh mainland
and is considerably less probable than the epicenter chosen by
the method of outlined in Data and Methods, given our current
understanding of the regional tectonics.
We find however, that the optimal epicenter is sensitive
to the values of intensities assigned to points north of the
epicenter. Three of these points are mentioned telegraphically by MacMurdo (1823) and lend themselves to debate.
The Martin and Szeliga (2010) catalog conservatively assigns intensity V to the southern two locations based on the
statement by MacMurdo that shaking there was less severe
Umarkot
8.6
25˚
8.4
Baliari
8.2
Allah Bund
8.2
24˚
8.1
8 8.0
8.0
Island Belt Fault
2001 Bhuj
7.8
23˚
25 km
68˚
Figure 11.
Figure 10.
The location of the 1803 Uttarkashi earthquake, as
determined by the method outlined in Data and Methods. The contours represent the 50% and 67% confidence contours, as determined by Bakun (1999). The instrumental epicenters of the 1991
Uttarkashi and 1999 Chamoli earthquakes (stars) are shown for
reference. The location of the 1803 Uttarkashi earthquake as determined by Ambraseys and Douglas (2004) is illustrated by a square.
We reject the alternative epicentral location permitted by the data
near the Ganges (indicated by the closed 50% and 67% confidence
contours). Filled circles indicate the locations of felt reports for the
1803 earthquake within 250 km of the epicenter.
8.2
7.6
22˚
69˚
70˚
71˚
72˚
73˚
Possible locations for the 1819 Allah Bund earthquake, as determined by the method outlined in Data and Methods
(open arrows with calculated Mw ). The parameters of these possible
locations are listed in Table 3. Black triangles (on the hanging wall),
locations of the fault responsible for the 2001 Bhuj Mw 7.6 earthquake (Schmidt and Bürgmann, 2006) and the Allah Bund fault
(Malik et al., 2001); dashed line, location of the inferred Island Belt
fault (Malik et al., 2001); filled circles, felt-intensity locations within 300 km of the epicenter; arrows, the change in epicentral location
due to changes outlined in Table 3. Contours represent magnitudes
from the epicentral location algorithm (Data and Methods) using the
raw intensity data; they indicate a minimum magnitude location in
the Gulf of Kachchh. The locations of Umarkot and Baliari are
shown for reference.
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
579
Table 2
Intensity Attenuation Relationship Coefficients Obtained by Other Investigations
Used in This Article
Article
Number of Events
Bakun and Wentworth (1997)
Bakun et al. (2003)
Ambraseys and Douglas (2004)
22
28
23
a*
3.67
1.41
0.46
b*
1.17
1.68
1.54
c*
d*
0
0:00345
0:004
3:19
2:08
2:54
†
*Columns a, b, c, and d refer to the variables in equation (1). The form of the attenuation
relationship used by Atkinson and Wald (2007) and its associated coefficients are listed in
Table (1) and equation (1) in Atkinson and Wald (2007).
†
This parameter was defined to be zero.
than on the Kachchh mainland. However, MacMurdo did not
personally travel north of the Rann of Kachchh, and damage
to masonry forts on the Kachchh mainland near Anjar
and Bhuj suggest intensities as high as IX (Bilham, 1998;
Ambraseys and Douglas, 2004). Thus, intensities to the north
of the epicenter could reasonably be as high as VIII and still
remain consistent with MacMurdo’s assertion.
Accordingly, we experimentally examined the shift in
location caused by increasing the assigned intensities at
the two closest locations just north of the Bund (Table 3).
The resulting shifts in epicentral location illustrate how sensitive the solution is to the sparse northern data. In each case,
the minimum magnitude location lies in the Gulf of Kachchh
and yields a magnitude of Mw 7.6. This location can be dismissed as inconsistent both with recent microseismic and
tectonic data and with available historical information. As
the intensities at Baliari and Umerkot are increased, the preferred epicentral location passes north of the easternmost
projection of the Allah Bund, and the magnitude increases,
eventually attaining a magnitude of Mw 8.2.
The credibility of these solutions, however, is diminished by the disquieting sensitivity of the solution to intensities north of the Allah Bund and the complete absence of
observations to the west. It is doubtful that our knowledge of
the shaking intensity at these locations or locations to the
west and northwest of the Bund will be significantly improved in the future due to an absence of detailed historical
records in the region. Thus, although our analysis using the
Table 3
Epicentral Locations and Intensity Magnitudes (MI ) of the
1819 Allah Bund Earthquake Determined Using the Method
Outlined in Data and Methods*
EMS-98
Latitude
Longitude
Depth (km)
MI
Baliari
Umarkot
23.67
23.77
23.85
24.12
70.58
70.56
70.39
70.21
15.00
15.00
15.00
15.00
8.0
8.0
8.1
8.2
5
6
7
8
5
6
6
7
*Uncertainty in descriptions of damage to the towns of Baliari
and Umarkot in MacMurdo (1823) permit a range of EMS-98
intensities, with a resulting range in the epicentral location and
magnitude for the 1819 earthquake (Fig. 11).
methods outlined in the Data and Methods section favors
8:0 ≤ Mw ≤ 8:2 and a location to the east of the Allah Bund,
we are skeptical of the result due to deficiencies in the observations. Of note, however, is the result that the magnitude
corresponding to the minimum deviation location appears to
overestimate the probable true magnitude.
The 1833 and 1866 Nepal Earthquakes
On 26 August 1833, three earthquakes shook the Kathmandu Valley—the first sufficiently alarming to bring people
out of doors, the second (5 hours later) alarming enough to
keep them there, and the third (occurring just 15 minutes
later) being the most destructive. Bilham (1995) estimated
the 1833 mainshock to be 7:7 0:2 using the methods
of Johnston (1996), while Ambraseys and Douglas (2004)
calculate a magnitude of Mw 7.6 with an epicenter 40 km
east of Kathmandu (27.7° N, 85.7° E). We infer a preferred
magnitude of M 7:3 0:1 with a location nearly 80 km east–
southeast of Kathmandu (27.553° N, 85.112° E) (Fig. 12).
Our calculated location roughly corresponds to the location
inferred by Bilham (1995); however, our calculated magnitude is smaller than that inferred by both Bilham (1995) and
Ambraseys and Douglas (2004). Although epicenters for the
two foreshocks are poorly constrained, using the assumption
that they occurred within the source region of the main shock
yields magnitudes of M 5.1 and M 6.5 respectively.
A moderate earthquake occurred on 23 May 1866 near
Kathmandu that is mentioned by several authors (Oldham,
1883; Khattri and Tyagi, 1983; Khattri, 1987; Rajendran
and Rajendran, 2005). Khattri (1987) assesses the magnitude
of the 1866 event as M 7.6, based on rupture length–
magnitude scaling relationships (Wyss, 1979). Although our
epicentral location is poorly constrained due to a lack of
observations north of Kathmandu, our data are consistent
with an epicentral location within 80 km of Kathmandu
and a magnitude of 7:2 0:2 (Fig. 12). Thus, according
to our intensity analysis, the 1833 and 1866 earthquakes
both appear to have ruptured similar locations in the Nepal
Himalaya with similar magnitudes. In this case, unlike the
1803/1991 earthquake pair, the slip in the second event
would not have developed over the course of 33 years with
a geodetic convergence rate of 18 mm=yr (Jade et al., 2004).
580
W. Szeliga, S. Hough, S. Martin, and R. Bilham
distances than those predicted by the attenuation relationship;
and, in particular, median intensity observations between
200 km and 875 km (median distances for intensities 4–7)
appear between one-half to one intensity unit greater than
anticipated.
Four possible explanations for the discrepancy illustrated
in Figure 13 are:
1. Intensities for the Bhuj earthquake were systematically
overestimated.
2. There is, or can be, a nonlinear dependence of intensities
on magnitude for large earthquakes.
3. Intensity observations at regional distances are amplified
by the presence of higher-mode surface (Lg) waves.
4. The intensity observations for the Bhuj earthquake
indicate a high-Q in the Kachchh Basin.
The 26 January 2001 Bhuj, India, earthquake is the largest calibration event that we used to determine attenuation for
cratonic earthquakes and the only cratonic calibration event
above magnitude 7 (Fig. 2). Although it appears to be circular reasoning to use our inferred attenuation relation to
determine an optimal location and magnitude for this earthquake, this is a potentially interesting exercise because the
attenuation relation is primarily constrained by events with
Mw ≤ 6 (Fig. 2). The intensity-derived location for the Bhuj
earthquake using intensity values from the Martin and Szeliga (2010) catalog yields a location only 12 km away from
the instrumental epicenter. This is slightly larger than the
grid spacing (9 km) used in the epicentral location method.
However, the magnitude is estimated as Mw 8.0 when using
the attenuation relationship derived only from earthquakes in
the Indian craton and as Mw 8.6 when using the attenuation
relationship derived for all of India. Thus, even though the
Bhuj intensities are used to constrain the attenuation relation,
the method of Bakun and Wentworth (1997) overpredicts the
magnitude of this event by 0.4 or 1.0 Mw units.
To explore why we obtain an unreasonably large magnitude for the Bhuj earthquake (and by implication, an uncertain
magnitude for the nearby 1819 Allah Bund earthquake), we
examine the intensity values for the 2001 earthquake as a
function of distance. The decay in intensity with distance
shows a systematic difference with the intensities anticipated
by equation (1) for a Mw 7.6 earthquake (Fig. 13). Moderate to
small intensity observations are found at significantly greater
Frequency (%)
The 2001 Bhuj Earthquake (Mw 7.6)
50
50
25
25
0
0
10 9 8 7 6 5 4 3 2 1
0
MSK
500
1000
1500
Distance (km)
2001 Bhuj Mw 7.6
10
9
8
EMS−98
Figure 12. The locations of the 1833 and 1866 Nepal earthquakes (stars) as determined using the method outlined in Data
and Methods. Contours, the 50% and 67% confidence regions obtained using method described by Bakun (1999); square, previous
estimate of epicentral location for the 1833 earthquake from Ambraseys and Douglas (2004); filled circles, locations of felt reports
for the 1833 and 1866 earthquakes within 250 km of Kathmandu.
We shall address each possibility in turn. First, we consider it unlikely that the intensities for the Bhuj earthquake
were systematically overestimated. Most of the values for
Bhuj in the Martin and Szeliga (2010) catalog are, in fact,
systematically lower than the values inferred by Hough et al.
(2002), whose intensity assignments were based on media
7
6
5
4
3
2
0
150 300 450 600 750 900 1050 1200 1350 1500
Distance (km)
Figure 13.
Intensity observations of the 2001 Bhuj Mw 7.6
earthquake compared to the attenuation curve derived for cratonic
India for an earthquake of Mw 7.6 (solid line). Open circles,
observed intensities; diamonds, median distance for each observed
intensity level; dashed lines represent the 2 σ envelope of uncertainty in the intensity attenuation model as a function of distance.
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
reports and have been shown to be biased relative to those
estimated from direct surveying of damage (Hough and
Pande, 2007).
Second, the functional form of equation (1) is identical
to the functional form assumed for attenuation of peak
ground acceleration (Evernden et al., 1973). Several studies
have shown a good correspondence between intensity and
instrumentally determined ground motion measures (e.g.,
Wald et al., 1999b). One, therefore, might reasonably expect
equation (1) to be appropriate for characterizing intensity
attenuation for large events. Short of significant nonlinearity
associated with ground motions at sediment sites, equation (1) appears to be appropriate for characterization of peak
ground acceleration for large and small earthquakes.
Third, when higher-mode surface wavetrains develop
and propagate in the continental crust, the highest amplitude
shaking typically has a long duration. It is thus reasonable, if
not expected, that a prolonged Lg wavetrain with a given
peak acceleration will produce a higher intensity observation
than will ground motions with the same peak acceleration
and a much shorter duration. Shaking duration will clearly
be a potential factor for structural damage; it is self-evident
that marginally perceptible shaking is more likely to be felt if
the strongest amplitudes are prolonged. Clearly, human perception of higher-mode surface waves decreases with distance from the epicenter by a noninteger amount. Thus, a
simple, uniform adjustment of intensity observations to
correct for amplification is not possible.
Lastly, we can consider the possibility that the intensity
distribution reflects especially high-Q in the Kachchh Basin.
Bodin et al. (2004) calculate Q for the Kachchh Basin using
aftershocks of the 2001 Bhuj earthquake and note that their
estimates are higher than estimates of Q in northern India
calculated by Singh et al. (1999). In contrast, in a regional
study of Lg attenuation, Pasyanos et al. (2009) shows values
of Q in the Kachchh Basin to be closer to those measured in
northern India (Singh et al., 1999). Additionally, results in
Mitra et al. (2006) indicate that estimates of Q from the
2001 Bhuj earthquake itself are systematically higher than
estimates from other regional events. To test the possibility
that the attenuation properties of the Kachchh Basin affect
intensity observations and consequently inflate the calculated magnitude of the 2001 Bhuj earthquake, we removed
all intensity observations within 200 km of the Bhuj epicenter and inverted for magnitude. The removal of all observations within 200 km of the epicenter results in an increase in
epicentral location uncertainty but essentially no change in
magnitude. This is not surprising because equation (1) indicates that a change in magnitude will have a larger influence
on distant, lower intensity observations than on near-source
high intensity observations.
For large earthquakes, locations are well determined
where sufficient spatial coverage exists. However, the magnitudes of large events are not well determined using the method
outlined in Data and Methods and require consideration.
As shown in Figure 13, the intensity values do not generally
581
match the intensities predicted by equation (1) for an Mw 7.6
earthquake between distances 200 km and 875 km from the
epicenter. In addition, the inferred intensity distribution includes moderate intensities to significantly greater distances
than the predicted distribution. The lowest felt intensities
(II–III) similarly extend farther than predicted. These results
suggest that the formation of higher-mode surfaces waves due
to long shaking durations in a high-Q environment have
amplified intensity observations at regional distances. Simple
correction of this amplification is not possible; moreover,
these results provide a caution regarding the use of the Bakun
and Wentworth (1997) method with an attenuation relation of
the form given by equation (1). In particular, if the attenuation
relation is constrained largely or entirely by small or moderate
earthquakes, the magnitudes estimated for large historical
earthquakes can be grossly overestimated.
Discussion
The determination of the magnitudes of historical earthquakes is of interest because, were a complete inventory of
historical earthquakes available, we could subject a region to
investigations of moment release over space and time.
Statistical tests assuming a Gutenberg–Richter distribution
of magnitudes show that we are missing 30% of the moderate
earthquakes during the period for which most of data are
derived (1800–2000). Thus, while moment-release studies
can be undertaken for the entire region, they are doomed
to be less reliable on a local scale, in particular for the relatively frequent 6:5 ≤ Mw ≤ 7:5 events that are typically
important for controlling probabilistic hazard.
The caveat discussed in the previous section, that our
attenuation findings for small earthquakes do not provide
satisfactory predictions for the attenuation observed in the
largest earthquakes and therefore yield unsatisfactory magnitude predictions, is perceived to be a substantial problem
in India because it is for these largest earthquakes that reliable magnitude information is most needed. It is possible that
a similar problem exists with the intensity relations established for North America.
Epicentral locations determined using the methods we
describe show demonstrable scatter. One question that arises
in the determination of magnitude and epicentral location for
early earthquakes is what constitutes an acceptable determination of these parameters. If we are interested in establishing
an inventory of potentially active faults, we should presumably prefer locations that lie within one source dimension
(e.g., a fault rupture length) of the earthquake. If we are
interested in identifying segments of those faults that remain
unruptured, we require yet higher accuracy. It is clear from the
analysis we present here that few of our post-1950 solutions
for earthquakes with Mw < 6 are within one fault length of the
instrumental epicenter, and, by implication, we must assume
that the same is true of the earthquakes earlier in the catalog.
For many of the events in the catalog with poor intensity
coverage, we do not attempt to determine a location using
582
W. Szeliga, S. Hough, S. Martin, and R. Bilham
quantitative methods. Yet even for these earthquakes we
recognize that the approximate location and its intensity data
are of utility in seismic hazard studies. Martin and Szeliga
(2010) utilize this information to map maximum shaking
intensity encountered in a grid throughout India.
In general, for larger earthquakes (7 < Mw < 8) where
rupture lengths range from 30 km to 300 km, we find that
our preferred location lies near or above the inferred rupture
surface; however, we note that, even for some very large
earthquakes in the catalog, the dimensions and location of
the rupture zone remain enigmatic (e.g., the Chittagong
1762 and Bihar-Nepal 1934 earthquakes).
For 100 earthquakes in the instrumental period (post1950) for which we have both epicentral parameters and intensity data, we find that fewer than 30% of these earthquakes
can be located to within one fault length of the true epicenter
using intensity data. The median mislocation error using the
method of Bakun and Wentworth (1997) exceeds 100 km;
however, choosing the minimum magnitude location instead
of the minimum deviation location reduces the misfit by a factor of 2. The reason for the poor performance of the algorithm
is partly due to the small number of observations available for
many of these earthquakes, as well as the small dynamic range
of the intensity observations for each earthquake. We conclude the algorithm cannot be expected to do better for historical earthquakes; location accuracies are likely to be no better
than 50 km. One disappointing result is that, from the data
alone, there seems to be no reliable way to characterize the
quality of each solution. In general, earthquakes with fewer
than 10 locations gave consistently unreliable locations.
We found that the most unreliable solutions were those where
large differences were found between the minimum deviation
location and the minimum magnitude location. The best locations were found to be those in which these two locations
agreed to within 30 km, but this applies to fewer than 30%
of the data.
Conclusions
Newly available intensity observations for India provide
a wealth of material for evaluating the location and magnitude of numerous earthquakes that have hitherto been amenable only to qualitative analysis and, in particular, permit us
to assess attenuation throughout the subcontinent. We use an
attenuation relation derived from modern (post-1950) earthquakes with well-determined instrumental locations and the
method of Bakun and Wentworth (1997) to estimate the optimal locations and magnitudes for 181 historical earthquakes, with case studies of large events in 1803, 1819,
1833, and 1866.
Of particular interest are the characteristic attenuationversus-distance parameters for India. We quantify attenuation for all Indian earthquakes and separately for plate
boundary events (Himalaya) and cratonic events. We find
that intensity attenuation in the Himalaya region is comparable to that in California, while attenuation in cratonic India
is significantly higher than attenuation in the central/eastern
United States.
One unexpected finding is that, for the largest of the
cratonic earthquakes (Bhuj 2001 and Allah Bund 1819),
our attenuation relation significantly overestimates the magnitudes estimated from instrumental and/or geological constraints. This results from shaking being felt more strongly
out to greater distances than expected by our attenuation
relationship. We suggest that this may be a systematic effect
that is common to all attenuation models. The distant shaking
from large earthquakes is not simply not well characterized
by shaking from small earthquakes. We propose that the
duration of Lg shaking at large distances may be responsible
for this effect.
Our search for uncertainty criteria to describe location
accuracy is unsatisfactory in that we have found no objective
method from the intensity data alone to quantify the accuracy
of our solutions. Where more than 100 intensity values are
available, the solution is usually within 30 km of the true
epicenter. This criterion applies to only 16 events, less than
3% of the catalog. Where the minimum deviation and minimum magnitude solution are close, the calculated epicenter
is usually within 30 km of the instrumental location, but even
this condition applies to less than 30% of the instrumental
catalog and, by extension, to fewer than 177 of the 570 earthquakes in the entire catalog.
The magnitudes of earthquakes in the instrumental
period were not well characterized by the Bakun and Wentworth (1997) algorithm. This is perhaps not too surprising
because the assigned magnitude for a given attenuation
depends on distance, which as summarized previously shows
a large range of mislocation errors. Magnitudes were in general overestimated by a median mismatch of 0.4 for the 100
earthquakes for which instrumental magnitudes were known.
The median magnitude misfit using the minimum magnitude
location underpredicts the instrumental magnitude by
Mw 0.6. Again, this uncertainty in magnitude suggests that
historical earthquakes cannot be characterized to better than
Mw 0:5 from the historical data analyzed here.
Data and Resources
Intensity distributions for moderate and large earthquakes occurring on the Indian subcontinent are available
from the Amateur Seismic Centre (http://www.asc‑india
.org). Data from the Global Centroid Moment Tensor Project
was retrieved from http://www.globalcmt.org; ISC and
MHDF catalog data were retrieved using SeismiQuery
www.iris.edu/dms/sq.htm. Figure 9 was created using gnuplot
(http://www.gnuplot. info/); all other figures were created
using Generic Mapping Tools (Wessel and Smith, 1998).
Acknowledgments
This research was supported by National Science Foundation-Division
of Earth Sciences grant no. 00004349. Doug Yule at California State University, Northridge, provided information on documented surface rupture.
Intensity, Magnitude, Location, and Attenuation in India for Felt Earthquakes since 1762
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Cooperative Institute for Research in Environmental Sciences (CIRES) and
Department of Geological Sciences
University of Colorado at Boulder
Boulder, Colorado
(W.S.)
U. S. Geological Survey
Pasadena, California
(S.H.)
Victoria University of Wellington
School of Geography, Environment, and Earth Sciences
Wellington, New Zealand
(S.M.)
CIRES and Department of Geological Sciences
University of Colorado at Boulder
Boulder, Colorado
(R.B.)
Manuscript received 17 November 2008